w^2-7w-9=0

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Solution for w^2-7w-9=0 equation: 


Simplifying
w2 + -7w + -9 = 0

Reorder the terms:
-9 + -7w + w2 = 0

Solving
-9 + -7w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -7w + 9 + w2 = 0 + 9

Reorder the terms:
-9 + 9 + -7w + w2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -7w + w2 = 0 + 9
-7w + w2 = 0 + 9

Combine like terms: 0 + 9 = 9
-7w + w2 = 9

The w term is -7w.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7w + 12.25 + w2 = 9 + 12.25

Reorder the terms:
12.25 + -7w + w2 = 9 + 12.25

Combine like terms: 9 + 12.25 = 21.25
12.25 + -7w + w2 = 21.25

Factor a perfect square on the left side:
(w + -3.5)(w + -3.5) = 21.25

Calculate the square root of the right side: 4.609772229

Break this problem into two subproblems by setting 
(w + -3.5) equal to 4.609772229 and -4.609772229.


Subproblem 1
w + -3.5 = 4.609772229

Simplifying
w + -3.5 = 4.609772229

Reorder the terms:
-3.5 + w = 4.609772229

Solving
-3.5 + w = 4.609772229

Solving for variable 'w'.

Move all terms containing w to the left, all other terms to the right.

Add '3.5' to each side of the equation.
-3.5 + 3.5 + w = 4.609772229 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + w = 4.609772229 + 3.5
w = 4.609772229 + 3.5

Combine like terms: 4.609772229 + 3.5 = 8.109772229
w = 8.109772229

Simplifying
w = 8.109772229


Subproblem 2
w + -3.5 = -4.609772229

Simplifying
w + -3.5 = -4.609772229

Reorder the terms:
-3.5 + w = -4.609772229

Solving
-3.5 + w = -4.609772229

Solving for variable 'w'.

Move all terms containing w to the left, all other terms to the right.

Add '3.5' to each side of the equation.
-3.5 + 3.5 + w = -4.609772229 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + w = -4.609772229 + 3.5
w = -4.609772229 + 3.5

Combine like terms: -4.609772229 + 3.5 = -1.109772229
w = -1.109772229

Simplifying
w = -1.109772229


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {8.109772229, -1.109772229}

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